year 8 maths

306 Chapter 5 Ratios and rates
12 Brontë can paint 15 m 2 in 20 minutes.
a What is the rate at which Brontë paints in m 2 /h?
b What area can Brontë paint in 20 hours?
c Brontë must paint 1000 m 2 in 20 hours. Find the rate at which she will need to paint in m 2 /min.
13 If x donuts cost $ y :
a H ow much would one donut cost?
b How much would one dozen donuts cost?
c How much would z donuts cost?
14 a A triangle has side lengths in the ratio 3 : 5 : 4 . If the longest side
is 35 cm, find the lengths of the other two sides and the perimeter
of the triangle.
b A triangle has side lengths in the ratio x : (x + 3) : (x − 2) . If the
shortest side is 17 cm , find the lengths of the other two sides and the
perimeter of the triangle.
15 In a faraway galaxy, a thriving alien colony uses the following units.
For money they have puks and paks: 1 puk (pu) = 1000 pak (pa)
For length they have doits and minidoits: 1 doit (D) = 80 minidoits (mD)
Polynaute rope is priced at 4 pu/D. Find the cost of the rope in terms of pa/mD.
ENRICHMENT
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16
Where will we meet?
16 Phil lives in Perth and his friend Werner lives in Sydney. The distance, by road, between their two
houses is 4200 km (rounded to the nearest 100 km ).
Phil decides to drive to Sydney and Werner decides to drive to Perth. They leave home at the same
time and travel the same route, but in opposite directions.
Phil drives at a constant speed of 75 km /h and Werner drives at a constant speed of 105 km /h.
a Will they meet on the road at a spot closer to Sydney or closer to Perth?
b How long will it take Phil to travel to Sydney?
c How long will it take Werner to travel to Perth?
d State the location of each friend after they have been driving for 15 hours.
e At what location (distance from Sydney and/or Perth) will they meet?
When they meet, Phil decides to travel in Werner’s car and they drive back to Werner’s home at an
average speed of 105 km /h.
f How long does it take Phil to travel to Sydney?
g Design a similar problem for two friends travelling at different constant speeds between two
different capital cities in Australia.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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